Subgroups — C₁₃×#22626 #15708965

Order 3328.

744 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1917	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1916	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1798	C₂	1	2	yes	maximal
7	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1750	C₂	1	2	yes	maximal
11	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#117	C₂²	1	2	yes	—
13	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
25	C₁₃×#384	C₄	1	1	yes	characteristic
26	C₁₃×#384	C₄	1	1	yes	characteristic
27	C₁₃×#382	C₄	1	2	yes	—
28	C₁₃×#380	C₄	1	1	yes	characteristic
29	C₁₃×#380	C₄	1	1	yes	characteristic
30	C₁₃×#380	C₄	1	2	yes	—
31	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#336	C₂²	1	1	yes	characteristic
35	C₁₃×#336	C₂²	1	1	yes	characteristic
36	C₁₃×#336	C₂²	1	2	yes	—
37	C₁₃×#336	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×#117	—	4	2	no	—
51	C₁₃×#117	—	4	2	no	—
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₁₃	—	2	2	no	—
63	C₂×C₄²×C₁₃	—	2	2	no	—
64	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊C₈	—	2	2	no	—
71	C₁₃×C₄⋊C₈	—	2	2	no	—
72	C₁₃×C₄⋊C₈	—	4	2	no	—
73	C₁₃×C₄⋊C₈	—	4	2	no	—
74	C₁₃×C₂²⋊C₈	—	2	2	no	—
75	C₁₃×C₂²⋊C₈	—	2	4	no	—
76	C₁₃×C₂²⋊C₈	Q₈	1	4	yes	—
77	C₁₃×#97	—	4	2	no	—
78	C₄×C₈×C₁₃	—	2	2	no	—
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₄×C₈×C₁₃	—	4	2	no	—
81	C₁₃×#95	C₂×C₄	1	2	yes	—
82	C₁₃×#95	C₂×C₄	1	2	yes	—
83	C₁₃×#95	C₂×C₄	1	2	yes	—
84	C₁₃×#95	C₂×C₄	1	2	yes	—
85	#22626	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	—	2	1	no	—
88	C₂²×C₄×C₁₃	—	2	1	no	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	4	1	no	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₁₃	#41	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
126	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
127	C₁₃×C₄⋊C₄	—	2	4	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₂²⋊C₄	—	4	2	no	—
136	C₁₃×C₂²⋊C₄	—	4	2	no	—
137	C₄²×C₁₃	—	2	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	2	1	no	—
140	C₄²×C₁₃	—	2	1	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₄²×C₁₃	#41	1	2	yes	—
146	C₄²×C₁₃	#41	1	2	yes	—
147	#2285	C₂×C₁₃	1	1	yes	characteristic
148	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#1917	C₂×C₁₃	1	2	yes	complemented
151	#1916	C₂×C₁₃	1	2	yes	complemented
152	#1798	C₂×C₁₃	1	2	yes	—
153	#1797	C₂×C₁₃	1	1	yes	characteristic
154	#1770	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#1750	C₂×C₁₃	1	2	yes	—
157	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic
158	C₂³×C₁₃	—	2	1	no	—
159	C₂³×C₁₃	—	2	1	no	—
160	C₂³×C₁₃	—	2	1	no	—
161	C₂³×C₁₃	—	2	1	no	—
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	—	2	1	no	—
164	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
165	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	4	4	no	—
192	C₂×C₄×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	#117	1	2	yes	—
194	C₂×C₄×C₁₃	#117	1	2	yes	—
195	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
196	C₂×C₄×C₁₃	#131	1	2	yes	—
197	C₂×C₄×C₁₃	#131	1	2	yes	—
198	C₂×C₄×C₁₃	#131	1	2	yes	—
199	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	2	2	no	—
207	C₈×C₁₃	—	4	1	no	—
208	C₈×C₁₃	—	4	1	no	—
209	C₈×C₁₃	—	4	2	no	—
210	C₈×C₁₃	—	4	2	no	—
211	C₂×#117	C₂²×C₁₃	1	2	yes	—
212	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
216	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
217	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
218	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#97	C₂²×C₁₃	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
224	#384	C₄×C₁₃	1	1	yes	characteristic
225	#384	C₄×C₁₃	1	1	yes	characteristic
226	#382	C₄×C₁₃	1	2	yes	—
227	#380	C₄×C₁₃	1	1	yes	characteristic
228	#380	C₄×C₁₃	1	1	yes	characteristic
229	#380	C₄×C₁₃	1	2	yes	—
230	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
231	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
232	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	#336	C₂²×C₁₃	1	2	yes	—
234	#336	C₂²×C₁₃	1	2	yes	—
235	#336	C₂²×C₁₃	1	2	yes	—
236	#336	C₂²×C₁₃	1	1	yes	characteristic
237	#336	C₂²×C₁₃	1	2	yes	—
238	#336	C₂²×C₁₃	1	1	yes	characteristic
239	#336	C₂²×C₁₃	1	2	yes	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	4	1	no	—
244	C₂²×C₁₃	—	4	1	no	—
245	C₂²×C₁₃	—	4	1	no	—
246	C₂²×C₁₃	—	4	1	no	—
247	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
249	C₂²×C₁₃	#518	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
251	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
252	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
253	C₂²×C₁₃	#568	1	1	yes	characteristic
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	4	1	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	#433	1	4	yes	—
263	C₄×C₁₃	#553	1	1	yes	characteristic
264	C₄×C₁₃	#553	1	1	yes	characteristic
265	C₄×C₁₃	#554	1	1	yes	characteristic
266	C₄×C₁₃	#554	1	1	yes	characteristic
267	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
268	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
269	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
273	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
274	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
276	#117	—	4	2	no	—
277	#117	—	4	2	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
279	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
286	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
287	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
291	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
293	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
294	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
296	C₄⋊C₈	—	2	2	no	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	4	2	no	—
299	C₄⋊C₈	—	4	2	no	—
300	C₂²⋊C₈	—	2	4	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	C₂²⋊C₈	Q₈×C₁₃	1	4	yes	—
303	#97	—	4	2	no	—
304	C₄×C₈	—	2	2	no	—
305	C₄×C₈	—	2	2	no	—
306	C₄×C₈	—	4	2	no	—
307	#95	C₂×C₄×C₁₃	1	2	yes	—
308	#95	C₂×C₄×C₁₃	1	2	yes	—
309	#95	C₂×C₄×C₁₃	1	2	yes	—
310	#95	C₂×C₄×C₁₃	1	2	yes	—
311	C₂×C₁₃	—	4	2	no	—
312	C₂×C₁₃	#2345	1	1	yes	characteristic
313	C₂×C₁₃	C₂×#433	1	1	yes	characteristic
314	C₂×C₁₃	#2924	1	1	yes	characteristic
315	C₂×C₁₃	#2960	1	1	yes	characteristic
316	C₂×C₁₃	#2962	1	1	yes	characteristic
317	C₂×C₁₃	#2979	1	1	yes	characteristic
318	C₂×C₁₃	#2981	1	1	yes	characteristic
319	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
332	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
334	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
335	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
340	C₂²×C₄	C₁₃×#41	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
359	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	C₁₃×#41	1	2	yes	—
379	C₄²	C₁₃×#41	1	2	yes	—
380	C₁₃	#22626	1	1	yes	characteristic, direct product factor, Sylow
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	C₄×Q₈×C₁₃	1	2	yes	—
388	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	C₁₃×#117	1	2	yes	—
417	C₂×C₄	C₁₃×#117	1	2	yes	—
418	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
419	C₂×C₄	C₁₃×#131	1	2	yes	—
420	C₂×C₄	C₁₃×#131	1	2	yes	—
421	C₂×C₄	C₁₃×#131	1	2	yes	—
422	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
424	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
425	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
426	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	2	2	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	2	no	—
433	C₈	—	4	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	C₂×C₁₃×#117	1	1	yes	characteristic
442	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
443	C₂²	C₁₃×#518	1	1	yes	characteristic
444	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
445	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
446	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
447	C₂²	C₁₃×#568	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	C₁₃×#433	1	4	yes	—
457	C₄	C₁₃×#553	1	1	yes	characteristic
458	C₄	C₁₃×#553	1	1	yes	characteristic
459	C₄	C₁₃×#554	1	1	yes	characteristic
460	C₄	C₁₃×#554	1	1	yes	characteristic
461	C₂	—	4	2	no	—
462	C₂	C₁₃×#2345	1	1	yes	characteristic
463	C₂	C₂×C₁₃×#433	1	1	yes	characteristic
464	C₂	C₁₃×#2924	1	1	yes	characteristic
465	C₂	C₁₃×#2960	1	1	yes	characteristic
466	C₂	C₁₃×#2962	1	1	yes	characteristic
467	C₂	C₁₃×#2979	1	1	yes	characteristic
468	C₂	C₁₃×#2981	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃×#1939	C₂	semidirect
3. C₁₃×#1939	C₂	semidirect
4. C₁₃×#1917	C₂	semidirect
5. C₁₃×#1916	C₂	semidirect
8. C₁₃×#1770	C₂	semidirect
9. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
85. #22626	C₁₃	direct (N × H)
148. #1939	C₂×C₁₃	semidirect
149. #1939	C₂×C₁₃	semidirect
150. #1917	C₂×C₁₃	semidirect
151. #1916	C₂×C₁₃	semidirect
154. #1770	C₂×C₁₃	semidirect
155. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
380. C₁₃	#22626	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#2285	2
C₁₃×#1939	2
C₁₃×#1917	2
C₁₃×#1916	2
C₁₃×#1798	2
C₁₃×#1797	2
C₁₃×#1770	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1750	2
C₄×C₁₃×C₂²⋊C₈	2
#22626	13

Subgroups — C13×#22626 #15708965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22626 #15708965